<p>The element-free Galerkin method (EFGM), a meshless approach, was applied to the stress analysis of adhesively bonded single-lap joints and compared with finite element method (FEM) and analytical solutions. EFGM successfully reproduced the general stress distributions, including three-dimensional effects such as anticlastic bending, free-corner stresses, and out-of-plane components that are not captured by classical analytical models. Error analysis revealed that FEM consistently provided closer agreement with analytical solutions, while EFGM exhibited larger quantitative discrepancies, particularly in σ_y and τ_yz. The novelty of this work lies in applying EFGM to the three-dimensional stress analysis of adhesively bonded joints, with a systematic comparison against FEM and analytical solutions, including explicit error analysis and evaluation of out-of-plane stress components. These results demonstrate that, although less accurate quantitatively, EFGM provides valuable qualitative insight and remains attractive for problems involving complex geometries or large deformations where mesh generation for FEM is difficult.</p> Graphical abstract <p></p>